Weihua Liu

Office: Mathematics Building, Room 715.
E-mail Address: weihualiu@math.arizona.edu
Mailing Address:
  • Department of Mathematics
  • The University of Arizona
  • Tucson, AZ 85721-0089

I finished my Phd in 2016 summer at UC Berkeley. My advisor is Prof. Dan-Virgil Voiculescu. Currently, I am a Postdoctoral Research Associate at the University of Arizona.

Here is my Curriculum Vitae.

I am interested in operator algebras, free probability, random matrices, operator theory, quantum groups.

(1). with Junde Wu, A representation theorem of infimum of bounded quantum observables. J. Math. Phys. 49 (2008).
(2). with Junde Wu, A uniqueness problem of the sequence product on operator effect algebra ε(H).J.Phys. A: Math. Theor. 42 (2009).
(3). with Junde Wu, On fixed points of Luders operation. J. Math. Phys. 49 (2009).
(4). with Junde Wu, On supremum of bounded quantum observable. J. Math. Phys. 49 (2009).
(5). with Junde Wu, Fixed points of commutative Lüders operations. J. Phys. A: Math. Theor. 43 (2010).
(6). A noncommutative De Finetti theorem for boolean independence. J. Funct. Anal. 269 (2015), no. 7, 1950–1994.
(7). Extended de Finetti theorems for boolean independence and monotone independence. Trans. Amer. Math. Soc. 370 (2018), no. 3, 1959–2003.
(8). General de Finetti type theorems in noncommutative probability Comm. Math. Phys. 369 (2019), no. 3, 837–866.
(9). with Qiang Lei, Zhe Liu and Junde Wu, Quantum Observable Generalized Orthoalgebras. arXiv:1508.07386 (to appear in Positivity).
(10). Free-Boolean independence for pairs of algebras. J. Funct. Anal. 277 (2019), no. 4, 994–1028.
(11).with Ping Zhong, Free-Boolean independence with amalgamation. arXiv:1712.02465 (to appear in Infin. Dimensional Anal. Quantum Probab. Relat. Top.).
(12). Free-free-Boolean independence for triples of algebras. arxiv.org(submitted).
(13). Operator valued random matrices and asymptotic freeness. arxiv.org(submitted).
(14). Relations between convolutions and transforms in operator-valued free probability. arxiv.org.(submitted)
(15). with David Jekel, An Operad of Non-commutative Independences Defined by Trees. arxiv.org.
(16). with Serban Belinschi, Hari Bercovici, The atoms of the free additive convolution of two operator-valued distributions. arXiv:1903.09002(a preliminary version).

Teaching I am teaching M 122B this semester.